backup and RAM
It is always a good idea to have your info backed up no-matter what. HD's fail and data gets lost and then it can be $1000's to get it back if you get it back at all. It is much cheaper to buy a external HD to backup every month or so with free software such as superduper!
That being said... The replacement process for the black and white MacBooks does not have the tech open the machine. It is a fairly simple process of removing the screen bezel and unscrewing the LCD and screwing in the new one. So there is almost a 0% chance of something happening to the HD directly related to the LCD replacement (unless the tech drops the computer).
The same goes for the RAM. If you are worried about the tech stealing it, take it out. Otherwise they don't open the computer to replace the LCD.
One last comment... pricing for screen replacement can be ridiculous. If you are paying more than $200 for the service, do it yourself. I offer the service here in LA, CA for $160, and still make a profit... If you are getting it done under warranty... that is the best price!